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JEE Math Practice Question

For any $$\theta \in \left( {{\pi \over 4},{\pi \over 2}} \right)$$, the expression $$3{(\cos \theta - \sin \theta )^4}$$$$ + 6{(\sin \theta + \cos \theta )^2} + 4{\sin ^6}\theta $$ equals :

  1. A.13 – 4 cos2$$\theta $$ + 6sin2$$\theta $$cos2$$\theta $$
  2. B.13 – 4 cos6$$\theta $$
  3. C.13 – 4 cos2$$\theta $$ + 6cos2$$\theta $$
  4. D.13 – 4 cos4$$\theta $$ + 2sin2$$\theta $$cos2$$\theta $$

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